Teaching

Splines and Approximation

Approximation Theory is the study of how general functions may be approximated or decomposed into more simple building blocks, such as polynomials, splines, wavelets, or other special functions. The course focus is analyzing how properties, such as smoothness or variation, of the function govern the rates of convergence of the approximating classes of functions. The explicit purpose of the course is to provide a foundation to mainstream classical analysis, as well as brief exposure to current areas of intensive mathematical activity, including such areas of computational mathematics.

Computer Aided Geometric Design

This course provides an introduction to computer-aided geometric design, which deals with the mathematical description of shape for use in computer graphics, numerical analysis, approximation theory, data structures, and computer algebra. Most concepts are fairly easy to grasp, others much harder. The concepts include basic geometric primitives, Bezier curves and surfaces, power and Bernstein polynomials, B-splines/NURBS, algebraic geometry, free-form deformation, subdivision, interpolation, approximation, surface intersection etal.

Mathematical Analysis

This course covers a branch of mathematics dealing with limits and related theories, which involves the elementary concepts and techniques of analysis. The basic concepts include real number theories, limits theories, one dimensional calculate, the definite integral, techniques of integration, sequences, series, techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals, the integration over regions, integrals over paths and surfaces, the change of variables formula, and integral theorems of Green, Gauss, and Stokes.

Calculate

This course covers very similar concepts as mathematical analysis excepte dealing with more computing parts.

Linear Algebra

This course covers basic concepts of linear algebra. Matrices, determinants, systems of linear equations, vector spaces, linear transformations, and eigenvalues etal.

Equations of Mathematical Physics

The theory of partial differential equations of mathematical  physics has been one of the most important fields of study in applied mathematics. This is essentially due to the frequent 
occurrence of partial differential equations in many branches of natural sciences and engineering.  This course covers provide students with the fundamental concepts, the underlying principles, and the techniques and methods of solution of partial differential equations of mathematical physics.

Wavelet Analysis

Wavelet is a mathematical technology developed in last 80th, which have important application in functional theory, differential equation, signal analysis and image processing. As a beginning course on wavelet analysis, the course includes Fourier analysis and transformation, Gabor transformation and wavelet transformation. The Mallat’s multi-resolution analysis, Daubechies’s orthogonal wavelet construction and wavelet package are introduced. In the end, some basic application of wavelet on image and geometric processing is discussed.